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Logical Atomism
Logical atomism is a philosophical view that originated in the early 20th century with the development of analytic philosophy. It holds that the world consists of ultimate logical "facts" (or "atoms") that cannot be broken down any further, each of which can be understood independently of other facts. Its principal exponent was the British philosopher Bertrand Russell. It is also widely held that the early works of his Austrian-born pupil and colleague, Ludwig Wittgenstein, defend a version of logical atomism, though he went on to reject it in his later ''Philosophical Investigations''. Some philosophers in the Vienna Circle were also influenced by logical atomism (particularly Rudolf Carnap, who was deeply sympathetic to some of its philosophical aims, especially in his earlier works). Gustav Bergmann also developed a form of logical atomism that focused on an ideal phenomenalistic language, particularly in his discussions of J.O. Urmson's work on analysis. The name for this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Philosophy
Analytic philosophy is a broad movement within Western philosophy, especially English-speaking world, anglophone philosophy, focused on analysis as a philosophical method; clarity of prose; rigor in arguments; and making use of formal logic, mathematics, and to a lesser degree the natural sciences.Mautner, Thomas (editor) (2005) ''The Penguin Dictionary of Philosophy'', entry for "Analytic philosophy", pp. 22–23 It is further characterized by an interest in language, semantics and Meaning (philosophy), meaning, known as the linguistic turn. It has developed several new branches of philosophy and logic, notably philosophy of language, philosophy of mathematics, philosophy of science, modern predicate logic and mathematical logic. The proliferation of analysis in philosophy began around the turn of the 20th century and has been dominant since the latter half of the 20th century. Central figures in its historical development are Gottlob Frege, Bertrand Russell, G. E. Moore, and L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (; ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the " father of modern analysis". Despite leaving university without a degree, he studied mathematics and trained as a school teacher, eventually teaching mathematics, physics, botany and gymnastics. He later received an honorary doctorate and became professor of mathematics in Berlin. Among many other contributions, Weierstrass formalized the definition of the continuity of a function and complex analysis, proved the intermediate value theorem and the Bolzano–Weierstrass theorem, and used the latter to study the properties of continuous functions on closed bounded intervals. Biography Weierstrass was born into a Roman Catholic family in Ostenfelde, a village near Ennigerloh, in the Province of Westphalia. Karl Weierstrass was the son of Wilhelm Weierstrass and Theodora Vonderforst, the former of whom was a government official and both of whom were Cat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal (metaphysics)
In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things. For example, suppose there are two chairs in a room, each of which is green. These two chairs share the quality of "wikt:chairness, chairness", as well as "greenness" or the quality of being green; in other words, they share two "universals". There are three major kinds of qualities or characteristics: type (metaphysics), types or kinds (e.g. mammal), property (metaphysics), properties (e.g. short, strong), and relation (metaphysics), relations (e.g. father of, next to). These are all different types of universals. Paradigmatically, universals are ''abstract (philosophy), abstract'' (e.g. humanity), whereas particulars are ''concrete (philosophy), concrete'' (e.g. the personhood of Socrates). However, universals are not necessarily abstract and p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Particular
In metaphysics, particulars or individuals are usually contrasted with ''universals''. Universals concern features that can be exemplified by various different particulars. Particulars are often seen as concrete, spatiotemporal entities as opposed to abstract entities, such as properties or numbers. There are, however, theories of ''abstract particulars'' or '' tropes''. For example, Socrates Socrates (; ; – 399 BC) was a Ancient Greek philosophy, Greek philosopher from Classical Athens, Athens who is credited as the founder of Western philosophy and as among the first moral philosophers of the Ethics, ethical tradition ... is a particular (there's only one Socrates-the-teacher-of-Plato and one cannot make copies of him, e.g., by cloning him, without introducing new, distinct particulars). Redness, by contrast, is not a particular, because it is abstract and multiply instantiated (for example a bicycle, an apple, and a particular woman's hair can all be red). In th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statement (logic)
In logic and semantics, the term statement is variously understood to mean either: #a meaningful sentence (linguistics)#By_function_or_speech_act, declarative sentence that is Truth, true or false (logic), false, or #a proposition. Which is the ''Denotation, assertion'' that is made by (i.e., the Meaning (linguistics), meaning of) a true or false declarative sentence. "A statement is defined as that which is ''expressible'' by a ''sentence'', and is either true or false... A statement is a more abstract entity than even a sentence type. It is not identical with the sentence used to express it... [That is,] different sentences can be used to express the same statement." In the latter case, a (declarative) sentence is just one way of expressing an underlying statement. A statement is what a sentence means, it is the notion or idea that a sentence expresses, i.e., what it represents. For example, it could be said that "2 + 2 = 4" and "two plus two equals four" are two different sente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Fact
In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences. For example, "The dog ran" is atomic whereas "The dog ran and the cat hid" is molecular in natural language. From a logical analysis point of view, the truth of a sentence is determined by only two things: * the logical form of the sentence. * the truth of its underlying atomic sentences. That is to say, for example, that the truth of the sentence "John is Greek and John is happy" is a function of the meaning of " and", and the truth values of the atomic sentences "John is Greek" and "John is happy". However, the truth of an atomic sentence is not a matter that is within the scope of logic itself, but rather whatever art or science the content of the atomic sentence happens to be talking about. Logic has developed artificial languages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Definite Descriptions
In formal semantics and philosophy of language, a definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is ''proper'' if X applies to a unique individual or object. For example: " the first person in space" and " the 42nd President of the United States of America" are proper. The definite descriptions "the person in space" and "the Senator from Ohio" are ''improper'' because the noun phrase X applies to more than one thing, and the definite descriptions "the first man on Mars" and "the Senator from Washington D.C." are ''improper'' because X applies to nothing. Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content. Russell's analysis As France is currently a republic, it has no king. Bertrand Russell pointed out that this raises a puzzle about the truth value of the sentence "The present King of France is bald." The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-existence
Existence is the state of having being or reality in contrast to nonexistence and nonbeing. Existence is often contrasted with essence: the essence of an entity is its essential features or qualities, which can be understood even if one does not know whether the entity exists. Ontology is the philosophical discipline studying the nature and types of existence. Singular existence is the existence of individual entities while general existence refers to the existence of concepts or universals. Entities present in space and time have concrete existence in contrast to abstract entities, like numbers and sets. Other distinctions are between possible, contingent, and necessary existence and between physical and mental existence. The common view is that an entity either exists or not with nothing in between, but some philosophers say that there are degrees of existence, meaning that some entities exist to a higher degree than others. The orthodox position in ontology is that e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexius Meinong
Alexius Meinong von Handschuchsheim (; 17 July 1853 – 27 November 1920) was an Austrian philosopher, a realist known for his unique ontology and theory of objects. He also made contributions to philosophy of mind and theory of value. Life Alexius Meinong's father was officer Anton von Meinong (1799–1870), who was granted the hereditary title of Ritter in 1851 and reached the rank of Major General in 1858 before retiring in 1859. From 1868 to 1870, Meinong studied at the Akademisches Gymnasium, Vienna. In 1870, he entered the University of Vienna law school where he was drawn to Carl Menger's lectures on economics. In summer 1874, he earned a doctorate in history by writing a thesis on Arnold of Brescia. It was during the winter term (1874–1875) that he began to focus on history and philosophy. Meinong became a pupil of Franz Brentano, who was then a recent addition to the philosophical faculty. Meinong would later claim that his mentor did not directly influence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Principles Of Mathematics
''The Principles of Mathematics'' (''PoM'') is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical. The book presents a view of the foundations of mathematics and Meinongianism and has become a classic reference. It reported on developments by Giuseppe Peano, Mario Pieri, Richard Dedekind, Georg Cantor, and others. In 1905 Louis Couturat published a partial French translation that expanded the book's readership. In 1937 Russell prepared a new introduction saying, "Such interest as the book now possesses is historical, and consists in the fact that it represents a certain stage in the development of its subject." Further editions were published in 1938, 1951, 1996, and 2009. Contents ''The Principles of Mathematics'' consists of 59 chapters divided into seven parts: indefinables in mathematics, number, quantity, order, infinity and continuity, space, matter and motion. In chapter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logicism
In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano. Overview Dedekind's path to logicism had a turning point when he was able to construct a model satisfying the axioms characterizing the real numbers using certain sets of rational numbers. This and related ideas convinced him that arithmetic, algebra and analysis were reducible to the natural numbers plus a "logic" of classes. Furthermore by 1872 he had concluded that the naturals themselves were reducible to sets and mappings. It is likely that other logicists, most importantly Frege, were also guided by the new theories of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
